I understand from the
orientation from the people present that they may be
more interested in the technicalities of the engine
than in the actual historical context of Babbage's
efforts. I'm afraid there's some medicine that I'm
going to have to administer and that is some history.
Because if there is a message about Babbage's efforts
at all, it's something that might be familiar to you
but is perhaps worth repeating.

And that's that the
face of innovation depends on issues that are other
than the technical merits of the invention. And if
there is a lesson from Babbage at all, it has to do
with that. So I'm afraid the unpleasant
aspects of medicine and history need to be administered
because, actually, why his engines are the way they are
and not otherwise and that is unfinished, is inseparable
from the context of his time -- who he was, who he
knew, his personality, the vendettas, the personal
conflicts -- were actually an inseparable part of the
story, why it is he failed.

In other words, there is no
technological determinist specific answers as to why he
failed. What we'll do in the course of the afternoon
is to actually explore some of those issues. So
much for preliminaries. So I apologize for the
history, and I will continue to do so, but it's a
necessary element in the story.

Babbage is celebrated as the great ancestral
figure in the history of computing, and almost every
lecture about Babbage starts with a statement of that
kind. He's famous equally for two things -- for the
genius of inventions, and
his failure to build any of them. His name is
inseparable from failure.

Babbage and
failure, genius and invention are all sort of one
package. It's one scrambled egg. He committed everything,
he staked everything -- his reputation, his
self-esteem, civil honors, money -- on one single
gamble. And that is he said, "Judge me by my engines".
And he failed to build them. He failed to communicate
a vision he had. He failed to communicate a vision of
what automatic computation he was capable of. He
failed to communicate it to his peers. He was deeply
embittered by absence of recognition, the failure of
civil honors.

And you will see we got some inkling in
the process of building this machine as to just how
extreme that disappointment must have been because it's
only through the process of building the machine and
actually witnessing it -- and you'll have an
opportunity of seeing the video -- that you begin to
understand the frustration and the despair he must have
felt in his inability actually to speak to anyone about
what it is he was doing.

He was unable to communicate
this vision, and therefore he was the first inhabitant
of a completely foreign country. The reasons for his
failure -- every book on the history of computing will
have a chapter or a passage on Babbage. Almost without
exception, you will read the same thing. Babbage failed
because of limitations of Victorian machine tool
technology. Almost without exception that is a
received perception.

When people go further, they
say -- and often they don't. There's just the --
either the implication or the explicit suggestion --
the reason the limitations of Victorian machine
tool technology entails that he could not make
parts with sufficient precision that when the machine
was built it would work. So people either implied that
or they specifically state it.

Now, there's something
very comforting in this thesis of limitations of
technology. From the high ground of microelectronics,
it's easy to patronize Babbage. Babbage had to wait
for us, the children of the Silicon age to rescue him
from his world of cogs and levers and wheels. E.B.
Thompson, the historian warned -- you see, he warned
against the enormous condescension of posterity, this
tendency actually to regard all that was past as
somehow inferior. And I think that through the -- so
credible as this thesis is and attractive as it is to
us, he failed limitations of technology.

It's like the
causes in science. It's a single cause has a direct
effect of failure. Credible as this thesis is and
attractive as it is to us and as self congratulative as
it is to us, Silicon is in fact is the legacy of the
life of Babbage. The fact of it is there is absolutely
no contemporary evidence that limitations of technology
was in fact a limiting factor if limitations of
technology is equated with limitations of precision.
Measurements done on contemporary machines show that
they were capable of the repeatability of one and a
half thousandths of an inch. That is to say, he gave
Joseph Clement, the engineer, a part of an intricate,
they could make other parts within one half thousandths
of an inch. The issue is, is one half thousandth of an
inch enough?

That's a highly precise thing. This was
England, the workshop of the world. And what we were
looking into one of the issues we had an opportunity to
evaluate is the extent to which precision was or wasn't
an issue. The fact is that the circumstances
surrounding the collapse of Babbage's major efforts to
build his engine. He conceived of the engine in 1821,
and he spent over a decade of design and development
building this machine.

The circumstances surrounding
the collapse of his efforts in 1833 do not owe anything
implicitly or explicitly to limitations of technology.
The circumstance are complex -- he had a dispute
with his engineer, Joseph Clement, over compensation
for moving the workshop from Lambeth to a special fire
proof workshop on the ground of Babbage's house. So the
circumstance are complex -- so when you remove the
technological *? * When you say, okay, if it is not
the limitations of engineering, what was it? You come up
with a very, very complex rich historical story. And
there are many elements to this story.

One of them is
personal vendettas that they in fact were advising the
government -- George Airy, the Royal Astronomer, persistently
and consistently was opposed and hostile to the utility
of these engines.

In other words, experts would disagree whether
these engines had any fundamental utility. Other
experts disagreed *, Sweeden said why do you need
engines that could calculate 30 or 50 decimal places?
One of his machines has double precision arithmetic,
multiplying a 50 digit number by another 50 digit
number, a hundred-digit result. Why did you need
precision of this kind when you could only measure to
three or four digits of accuracy?
So experts would
disagree about fundamental utilities.
It wasn't as
though there was a universally accepted problem to
which there was a solution that was needed.

Personal vendettas. Babbage was convinced that Airy's hostile
advocacy of his engines and his advice to government
that the engines were worthless was based on a personal
hostility of jealousy, and a particular court case
court case in which Babbage acted as an expert witness
against the party that was being advised by Airy.

And
Babbage makes these allegations public, the specifics
of it don't matter. The point about it is that there
are all these broad and peculiar factors involving
personalities, vested interests, that affected the fate
of the engines other than the specific merits of the
technology.

Runaway costs. There was little credible
progress. After 11 years he manufactured about 10,000
parts of the 25,000 needed. He had nothing to show.
The government invested large sums of money. This
money was unmanaged. There was no ceiling. There was
no budget. There was no delivery date. There were no
staging posts. There were no phrasing of stage
payments. He was just wonderfully muddled
and terribly English. [some laughter]

It's inconceivable in this day
and age with this obsession about cost efficiency and
all the other management gobbeldy gook that this
gentlemen's arrangement about funding a project to
completion on the good-faith basis could ever come
about. But it did.

So the fact of the matter is that
the limitations of technology -- attractive as that
thesis is to us -- is not a specific feature that
feature in the contemporary circumstances that resulted
in the collapse of this work. Clement downed tools after
complaining about compensation, and the work was never
resumed in 1833, after about 10, 11 years of design and
development.

The
question that becomes very tantalizing to historians is
did the complex circumstances surrounding the collapse
of the project to build the machine mask the technical
or logical possibility - feasibility, of this machine?
In other words, had people been distracted by either --
the question is: If people accepted that limitation
that technology was the reason and it turns out it is
not the reason, did circumstances surrounding the
collapse mask the fact that these engines could not
have been built? In short, the question is: Could the
machines have been built in Babbage's day? And,
secondly, if they had been built, would they have
worked? And that is the issue we actually set out to
address.

I promised that you would have some medicine
before we get onto the technology -- onto the actual
specifics of the machine. And so because the fate of
the engine is inseparable from the context of Babbage's
times, I'll just give you a quick thumbnail sketch of
Babbage's his life. Who was he? What was the context?
What were the circumstances? Why did he wish to build
these machines? It's very quick, and it's sort of --
without doing violence to the riches of any man's
life -- just sort of caricature a thumbnail sketch of
the man's life if you like.

[photo of babbage]
That's not Napoleon. It's Babbage in 1830 at age
21, undergraduate at Cambridge -- a spirited
undergraduate -- went there to study mathematics.
There's a lesson in Babbage's study of mathematics, and
that's -- he was -- Peahouse's crack man - he was a very
accomplished mathematician when he went to Cambridge.
He looked forward to having his puzzlements about
calculating and Continental theories illuminated by
his tutors, and he found that his tutors were state old
stuffy lot who weren't interested in Continental
mathematics. So he was quite a renegade. He arranged
his own program of study. He founded the Analytical
Society. He dedicated to the reform of English mathematics
which had quite an impact. He befriended John
Herschel, the astronomer, lifelong friend, George
Peacock. But there's an indiscretion he committed
which is not widely known. That is he was Peahouse's crack
man. He was expected to be a wrangler, this rather
obscure method of --

And in order to qualify -- students were ranked
according to ability by a preliminary set of
prestigious called The Acts in which you have to
defend, sometimes in Latin, a proposition against
opponents. And he chose to defend the thesis that God
was an ethereal agent. And this was regarded as
blasphemous, and he was disqualified. He was thrown
out.

He didn't leave Cambridge, but he qualified
without honors. The reason I mention
that tale is first, between these students, they ought
to be aware that principles sometimes have consequences
that are politically damaging to their futures. This
stopped any prospect -- I'm not suggesting they
compromise but they ought to be aware of the
consequences. This stopped any prospect Babbage having
an academic career. He couldn't get a fellowship, he
left with an ordinary degree. He was a top
mathematician, so you know he was going for the degree.

He later became Lucasian professor of mathematics, so it wasn't a
disastrous thing for him in career terms. The point
about it is that it set a pattern because that was not
the only time Babbage damaged his personal political
interests by public protest and sometimes ill
considered -- and it's not as though he was alone in
the radical views he held. John Herschel, George
Valerie held similar views. One of the views was that
they resented and resisted the notion that education
was dominated by the church, university education was dominated
by the church.

None of them wanted to take orders. In order to
take a fellowship, you had to become a member of the
church, take orders. Babbage was hostile to this but
so was Airy and so was Herschel. Both became hugely
successful contemporaries in science. I mean, Herschel
was a model ambassador for science. They shared
Babbage's view, but they were slightly more prudent in
their public expression.

And this pattern that Babbage
set repeated later far more damagingly and actually
affected the fate of the engine. So here I come again
with this horrible medicine looping back. We cannot
separate the fate of these engines from who Babbage was
and this proclivity he has for public protest. Most of
these writings are written really more to protest than
to persuade. He was indignant, he was highly principled,
uncompromising in principle.

And if there is a lesson
there, it is that there is a personal cost to high
principle, especially if you're politically inept.
[Much laughter]

Golly, at this rate, we're never going to get out of
here. So that's back in 1813. Georgiana, his wife,
married in 1814 just after he graduated in defiance of
his father he ran away and got married. He didn't
get along with his father at all. Georgiana tragically
died in 1827, and Babbage was quite bereft, never
really recovered, never remarried.

[image]
This is Babbage Lucasian professor of mathematics. So this is an
engraving by Roaf. Babbage occupied the Lucasian professorship
from 1828 to 1839. This is around 1830, 32. And it's
a highly idealized -- it doesn't look like that you'll
see from the images I'll show you presently.

And the point
about it is that he said that he was deeply resentful
of the fact that his peers did not acknowledge him. He
was not recognized for what he did.
It's perfectly clear he had a very clear
conviction he had discovered something fundamental
about the machine behavior, the stepwise algorithmic procedure. He
knew he had seen something. And he was unable to
communicate it with others. He was deeply resentful of
the fact that this was not acknowledged. And he said
of his appointment of Lucasian professor that this was the
only honor his country had bestowed upon him. And he
said this without bitterness. He was deeply gratified
for the chair. He didn't do anything, he never gave
any lectures while at Cambridge. That was a loophole in the
regulations, which have since been closed. [Laughter]

In 1830 he published a critique of science in England.
This was an absolutely vicious, vituperous, sarcastic
attack on the royal society on the side of
establishment. This was the same establishment that
was to support him three times in securing government
funding for his engines. So he had a fantastic habit
alienating the people of whose support he needed. He
somehow though that being right entitled him to be
rude.

He personally attacked the officers of the
society, accused them of fiddling the minutes, of
misappropriating -- of rigging the rules by which
awards were given. He accused Davey of personally
profiting from publications. It was a thoroughly
indiscreet -- it was not settled over brandy and cigars
as a gentlemen would. This was a public broadside, a
broadside of outrage and indignation about the
deficiencies of the society. So, again, we go back to
the resonance of what happened in Cambridge. So
that's -- now in 1832 -- 1830 he published the client
of science around the time of this thing.

1832
He published the "Economy of Machinery Manufactures". This
was an absolutely ground breaking book in political
economy and one of his most successful books. He was
established as an elder statesman of the industrial
movement. It's an extraordinary volume and did much as
it were to repair the damage that he had done with the
scientific establishment. After the publication of
decline he never -- he was a member of the royal
society from 1816 -- after that, he never went to the
royal society, never attended any meetings. In a
sense he excluded himself from the power base upon
which science was operating.

[image of Babbage] That's Babbage. And
that's an oil painting by Samuel Lawrence of the
national portrait gallery. That's Babbage in his early
50's, about 1843. This is Babbage as a man of science
in letters esteemed by his peers. He was very well
known. He was a celebrity. He was well published. He
published half a dozen very credible, not acclaimed but
well regarded, mathematical papers. He published in
all six monographs and 86 papers miscellaneous scientific and
mathematical.

So that's Babbage if you like at his height, very
credible figure, socialite of the London society, and
esteemed by his peers. That's very intriguing. That's
* by *Clowday and why it's significant for us is
because this was taken at the time he was designing
difference engine II, which is the machine we'll spend
if there is any time left on. And there you can see
he's still sort of combative, but he's weary. He's
been through a lot, but he's still up there designing.
He had by that time almost given up the prospect of
building an engine, but he was carrying on designing
them. So that's about 1849, 1850. So he's in his
early fifties there.

[image of Babbage] This is Babbage 1860. It's the last known
portrait of him at the Fourth International *
conference in London. It's what I call his Beethoven
look. It's grumpy. The first biography Babbage made
with Moseley in 1863, titled the book the "Irascible
Genius". And this is a caricature that has stuck.
Despite the scholarship sense, it is still the most --
the clearest and sharpest image of this man. And I'd
say it's still one of the snapshot of him is respite.

Okay. That brief, thumbnail sketch sort of traces
Babbage from an idealistic student into an esteemed man
of science into a venerable grump. And that is a very
brief account of his life. His father died 1827. 1827
was a staggeringly tragic personal tragic year for him.
His father, two of his children and his wife died all
in the same year. He effectively had a breakdown -- I
don't think they used those words and know quite what
the word means, but he went on a continental tour for
over a year with one of his workmen and stopped working
the engines.

He inherited a hundred thousand pounds
which was a staggering amount of money in those days.
If you think that -- a steam engine by Stephenson
shipped to the States in 1830, the * cost off-shelf,
brand new steam locomotive cost 784,000 shillings. He
inherited a hundred thousand pounds in modern day terms
you here to multiply that out 30 to 150. So he was
sort of near a millionaire. He was well able to afford
to fund the projects of his engines from his own
pocket. To a large extent, he did bankroll the
projects despite government money.

Okay. That's enough of Babbage. The medicine's
been taken. Thank you for being so gracious. And I
hope that it has the appropriate anxiety effect or be
cured of your obsession of technology. I meant that
facetiously.

Okay. Why did Babbage design engines? What were
they for? What was the whole movement about? That's a
page of mathematical tables from *Vega -- a lot of
tables from *Vega, 1794, typical of mathematical tables
at the time. And the point is how were these produced?

These tables are produced by hand. I mean, clearly
being typeset, but there were four stages in the
process of production of mathematical tables.
Mathematical tables are highly important. There were
no devices that you could produce -- do instant
calculation at the time and place of need. So almost
anyone in need of tables -- and that's insurers,
journeymen, tradesmen, scientists, engineers --
whatever they needed to do any calculation beyond
anything trivial, including * for fractions, multiples,
squares, cubes and all that. Absolutely relied to put
them into immediate communications paper and print.
And it's perhaps necessary to remind ourselves of that.

There was one particular application of tables which
was absolutely paramount and that was astronomical
navigation. Ships were reliant on tables for
determining their position at sea, capital and life was
at risk, England was a major seafaring nation, the navy
and merchant navy depended on accurate navigation.
Shipwrecks were a very serious fear, and these were
reported with graphic detail in public media,
illustrated London news, for instance. And the number
of gismos and gadgets to prolong life at sea off the
ship is astonishing. It's like America has endless
devices for keeping people vertical, for bringing fish
biting you, for doing all sorts of things. And clearly
there was a lot of public fear. So there was a deep
insecurity about shipwrecks.

Now, the few court
martials of ships going aground that I've looked at --
none of them specifically incriminate inaccuracy of
tables. It's always to do with the practice of
navigation or it's -- the fact was that there was this
deep fear. So the fear was that the tables were
riddled with errors. And the reason they were riddled
with errors was -- well, * and they look at errata
sheets. When errors were found, they printed errata
sheets and you could tell by analyzing the errata
sheets just how error riddled the tables were. And in
a random of selection of 140 volumes of tables, *
account 3,700 errors printed in errata sheets. He
hoots with uncontainable glee to discover that some of
the errata sheets had error themselves. And he's
utterly uncontainable when it turns out that the second
errata sheet also had errors. * errata, errata,
errata.

It was quite a credible position to hold
that these things were riddled with errors. Why they
were riddled with errors? Because of the method in
which they were produced. Tables were calculated by
hand by people who were called computers. It's known
people were computers, they weren't machines. Just as
typewriters were people rather than machines.

And so
firstly there was the risk of human error, the
fallibility.
We end up very bad at doing accurate
calculations especially repeated, tedious things like
repeated addition. From differences which is a
technique for generating these things.

The second
thing is you've got to write the answers down in the
table to give to a printer. So there was a possible
error of transcription, writing the results down.

Third source of error was typesetting. Each of these
digits is represented by loose type, by compositor.
It's possible to put them upside down, they fall out,
you put them in the back around. There is no
contextual thing to indicate -- it's no more likely
that one number is a six or a seven. It's not like a
word where somebody could recognize an error. So
there's no contextual information to indicate to the
compositor that it's wrong. So error of calculation,
error of transcription, error of typesetting.

Fourthly proofreading. How do you know the stuff is correct?
And anyone who's seen it, has seen the table some idea
just -- I mean, you might say okay it's not so bad
doing that. But you give some indication of (knock,
knock) that's the volume that that page came out of.

What confidence could you conceivably have if two
people tried to check tables of that kind? That's one
volume of just logarithms and trig functions. So
that's the problem. The problem was error in tables
and the solution for Babbage was mechanization,
engines, machines. So that's the entry point, if you
like. And the genesis episode.

How did this happen?
Did it come in a flash, you know, bolt of lightning,
flash of thunder? What? Something like that. He's
sitting with John Herschel, his good buddy, in 1821,
checking tables from the astronomical society. And
what you typically did you gave the same set of
calculations to two separate computers who, without
collaboration, computed the results separately, and you
compared them. If they were the same, doesn't mean
they were correct because there are a few instances
that two people make the same mistake. You had a high
degree of confidence that they were correct. And for
Herschel and Babbage sitting there in 1821, the summer
of 1821, in the rooms of the astronomical society,
checking the two results from the sets of computers.
And they were just amazed by the discrepancies. And
Babbage, as it were, clasps his hand to his head and
says, "I wish to God these calculations had been
executed by steam."

Okay. That was it. That was the rest of
his life. That phrase dominated the rest of his life.
He spent the rest of his life in one way or another
very intensively trying to calculate -- to produce
mechanized * way of printing mathematical tables. Now
steam was a method for mechanization. It wasn't that
these things would be solely driven by steam. No where
else in any of his writing have I found reference any
of these machines being driven by steam engine.

So steam was a method for mechanization.
It was the middle of the industrial revolution, England
was the workshop of the world, and so steam was
metaphorical in the literal uses of steam. So that was
the start. He then became obsessed. He became so
obsessed by these things that he actually became ill.
And he was advised by his medical friend to stop
thinking about engines, and he didn't.

Right. What was the state of play at the
time? Just how revolutionary is his conception? Just
how revolutionary is his conception of these things?
Well, it's probably well known that the earliest known
mechanical -- mechanical calculation received a huge
emphasis in the 17th Century. Schickard in 1623 made his
calculating clock, didn't survive. Earliest surviving
calculator is Pascal's pascaline, 1642. Sorry.
That's an arithmometer. Where's the pascaline? No.
Sorry. It's not there. The point about the pascaline
and likenesses -- and * calculator, 17th century. Is
that that they are or basically ornate curiosity.

That's a calculator by Müller, 1784 to give you some
indication it's based on likenesses of step wheel. And
these were ornate curiosities. They were totally
unsuited for routine or regular use. That's a
*universal calculator, does addition, multiplication,
does multiplication and repeat addition and so on.
These were objects of course quite a stir. They were
paraded through the salons of the elite,
Aristocracies, stimulated huge discussions about
mentalism and machines. But they were not work horses
for daily calculation.

The arithmometer which we have
there was the first commercially successful machine.
It wasn't commercially successful much later. It was
produced in 1820 from **Mr. Colmar. They were used in
vast numbers, made by the tens of thousands later in
the century, took many, many decades before they
actually caught on. So they were introduced this 1820
's first commercially successful calculator, they were
decades of development before they actually ironed the
bugs out of them. So 1820 just before the point at
which Babbage conceived this conception -- had this
great revelation that the onset this invocation of
steam to solve the problem of mathematical tables, this
was -- and that's a later one. A cruder version of
this was it. And the point about this is that it's
manual. It relies on the continuous informed
intervention of the operator to achieve useful results.
You have to use push the sliders, you have to turn the
handle a fixed number of times, you have to lift the
carriage, multiply by tens, you lift the carriage,
shift one indicator over. You could make a mistake and
shift it two.

You had to write the results down.
Transcription errors. So there's possibly operated and
it's a manual calculator relies in formed intervention
for getting useful results out of it. So that's the
big first step, was automation, to embody the
mathematical principal into the machine. And Babbage
conceived this difference engine number one, his first
difference engine, which is 1821. And that's what
ultimately -- (inaudible)
He spent 10, 11 years on design and
development of this machine. That was one seventh of
it. It's all that was assembled.

By 1832 he was
losing credibility, he had nothing to show. He asked
his engineer, Joseph Clement, to assemble something
from the parts and this is what resulted. It's
probably the most celebrated icon in the prehistory of
computing. It has that position for several reasons.
Firstly, it's a methodological standard. If you want
to know how precisely you could machine parts,
repeatability, accuracy, any kind of precision
manufacture, you do measurements from this machine. It
was made by Joseph Clement to the highest standards
available at the time. So it's a methodological
standard so it's a (inaudible) and historically
(inaudible).

It is also the first automatic calculator
that survived. There's a handle on top. You crank the
handle, you set the initial values, you crank the
handle, you get the results. Every time this machine
goes through one cycle it produces the next value of
the table by method of finite differences which I
assume is completely familiar to you. And I think I've
got a small trivial example to show you just in case it
isn't. All it does is by repeated addition evaluate
the polynomials, and we'll see how it does that. The
point about it is that it's the first machine to
successfully embody mathematical rule and mechanism.

The operator does not need to understand the
mathematical principle in which it's based or how the
machine works in order to get useful results. You
exert physical energy and you achieve results which up
to that point in time, you could only arrive at by
mental effort, by thinking. And the implications of
this were not lost by Babbage and his contemporaries.
They called it the thinking machine. And the marvelous
pulp and fiber of the brain had been substituted by
brass and iron. He, Babbage, had taught wheel work to
think. This was so said, **Harry Buxton, a junior
colleague of Babbage's. And so the implications of
this were not lost, I mean, the machine intelligence
was not lost on Babbage's contemporaries. So that's
difference engine number one.

Question from audience member -- inaudible.
So high. About two-feet high. The full
machine would be something like 11 feet high, 8-foot
deep, and weighed many, many tons.
Question from audience member -- inaudible.
Many tons. We don't know. I can tell you
that difference two [engine] specifically because we weighed
it. And this would be vastly heavier. The difference
two weighs five tons. And this was about three times
the weight. And this is three times more parts. So
we're talking about 10 to 15-tons when estimated.

Question from audience member: I guess
this was the first technician for artificial
intelligence?
Yes, I would say that's one of the original
artificial intelligence artifacts, yes.

Question from audience member: What was
the effect of (inaudible - laughter) --
We've redefined them. We've defined it as
the "Crick." And I'll come to the Crick, and I'll tell
you exactly what a Crick is. Crick is the name of the
engineer who cranked the handle. We know exactly how
many cricks these machines can run. There is a
conversion factor.

So that's difference engine one. I don't
think there's time. There's a wonderful -- I believe
it's history so it's probably unpleasant for you.
This machine featured in the development of
the history of ideas in a way that is not specifically
* technology but it had a huge impact. Babbage used it
to demonstrate his theory of miracles -- and I know
this is dangerous territory, especially in an
environment like this. Religion was under increasing
siege from science. Geology started producing in the
1830's, geology started producing evidence that the
earth was older than theologists had actually liked to
believe. So there were rifts and cracks appearing in
the edifice of religion. And the problem is how do you
reconcile rational science with theism?

How can you
both be a scientist and believe in God? And Babbage
used this machine in a very ingenious way, to try and
reconcile those two positions. And you see the problem
was with miracles, you see miracles are very good for
religion. They have fantastic PR. Because you don't
need -- science espouses the notion of physical cause.
Right? If God causes everything, it isn't a problem
because that's the explanation. Science says there's
physical cause. The problem is miracles manifest the
stress *(inaudible) science because they are events
without physical cause.

So on this science addressed
the issue of miracles, it was indeed trouble. And if
you like doing this wrestling match with an explanatory
receptor, they were competing with each other for the
accepted view of the world. And Babbage had an
absolutely ingenious way of showing that miracles --
the discontinuities in nature were not necessarily
manifestations of the mind intervention. What he did
was he set -- okay.

Babbage was a social liar. If you
wanted to know what was going on in science, in
literature, art religion, you went to Babbage swaray
center. They were the social events of the week.
Everyone was there, Darwin, McGreedy, anyone you can
think of was there. And social intellectual League of
London, the English Society, was at Babbage's. And
Babbage used this thing as a party trick. It sat on
his mantle piece and he cranked the handle. What he
did was he set the machine up to do something very
trivial like increment by two. So every time he turned
the handle, a number moved to two. And he'd do this
and very quickly people would become pretty inured to
the expectation of incrementing by two. So he'd crank
the handle, and he'd go by two, four, six, eight. And
he'd ask, you know, what do you think the next result
would be, and it would be there and by God. And he'd
do this endlessly. He'd do this a hundred times.
People began to get bored it was rather trivial. And
suddenly, without any intervention on his account at
all, the machine would form a discontinuity and
suddenly he had 117.

And he would turn to his people
and say, "You see, for you, the observers, that was a
violation of law. It was a violation of the law of
incrementing by two. But for me, the programmer, I
programmed that machine. And after 150 integrations,
it would do something discontinuous. And for me, the
programmer, that is not a violation of law, but a
manifestation of higher law, known to me but not to
you. By analogy, miracles in nature, discontinuities in
nature, are not violations of law, they're
manifestations of higher law. God's law is yet
unknown."

So for Babbage, God was a programmer, and
those in the software industry may be very flattered to
know that. Okay.

I apologize for the insulting
triviality of this next example.

Okay. Why method of differences? The
machine is called a difference engine because of the
principle of the -- it's so called because of the
principle on which it's based upon. Everyone know that
(inaudible) the derivative of a constant. That's --
right. Calculus stuff.

So the question is what special -- why is
the difference principle so important? The answer is
you can evaluate polynomials which ordinarily in the
evaluation of the various coefficients, constants -- of
the various coefficients, of the various powers, of the
unknown. Ordinarily you need multiplication, division,
subtraction, arithmetic -- and division to --
multiplication, subtraction, and addition to find the
value of the coefficient of the multiplies. Now the
point about -- now, doing direct multiplication and
division in mechanics is monumentally difficult. It's
something Babbage accomplished much later. The beauty
of the method of finite differences is it allows you to
find the value and tabulate values of polynomials using
repeated addition. And this trivial example -- and I
apologize again for the triviality.

Okay. Counting numbers. Oh, boy. X -- X
squared is the familiar table. Now assume that we've
generated up to 36. We want to generate the table of
squares. That's the object. The exercise -- so I've
got 1, 4, 9, 6, and 31. Say we've got up to 36. Well,
I mean, I apologize if all of this is familiar, but --
All right. You take successive difference.
4 minus 1 is 3, 9 minus 4 is 5 and so on, and so on.
The first column is the first difference. Second
column predictably is constant 2 it's the second order
of polynomials.

By working backwards, you add 2 to 11, 11
to 13, 13 to 13 -- you get 49. You get the next
element of the table having performed no
multiplication. Okay. That's a trick. Repeated
addition you can find the polynomial. Trivial example.
It's X squared, but the point is that Babbage's
machines and the one we built calculates to seven
orders of difference and 30 decimal places. Right? So
each of these digits is 30 to 31 figures long and
there's seven orders of difference.
So you can calculate so that the difference
in the two, for example, were designed to calculate and
tabulate a seventh order of -- any seventh order
polynomial, positive and negative coefficients, X plus
or minus, any seventh order polynomial with all terms
present to 30, 31 decimal figures of accuracy.

So that
was the ambition, and that's no slouch even by modern
standards. These were fixed point machines, but even a
modern calculator is -- overpowers any, all these other
things monumentally, you still can't get 31 digits of
significant figures out of it.

So we shouldn't be back to E.B. Thompson's
enormous condescension of (**). This was some no
small accomplishment to conceive of an engine with that
capacity. They didn't build them, of course. But we
remedied that.

Okay. These are decimal digital machines.
They use the digits in order to turn (***). He
considered all numbers including binary. He considered
duodecimal, X divisible, 8 bases of 5 -- he
considered all kinds of bases. He chose this for
reasons we can discuss presently. And the reason for
this slide is really to show the intense -- why it was
digital.

Okay. He only acknowledges discrete
states, whole numbers. So wheel -- okay. Numbers are
represented by figure wheels with engraved things on it
and teeth on them. And a wheel between 2 and 3 does
not represent 2.5. It represents an invalid state.
The point about it, these are not bi-stables. They're
not meta-stable things that flip automatically once a
threshold is exceeded.

These are analog devices. The
reason they're digital is the control system, and
here's an example. You can see this roller tries to
sandwich itself between two half-moons as it goes
around. That is how it digitized. The roller locks
and fixes it. Because it's a roll-on rather than a
wedge, it doesn't flip over once it actually goes
beyond a threshold. But you can begin to see why it's
digital is because that is what actually makes it
invalid. If that is obstructed by one of those half
moons sitting on the apex, the machine jams. So the
machine jamming is a form of error correction, and it's
a specific part of the control mechanism. The
discreetization of the state is through its controller,
not inherent lack of stability as you wouldn't be
saying in modern threshold, bi-stable, whatever. That's
1822.

Okay Babbage is not famous because of his
difference engines. He's famous because he was the
pioneer of computing. His difference engines are
calculators. You put numbers in, it crunches numbers
the only way it knows how is by repeated addition. So
it takes a column and adds it to another column and so
on. That's a calculator. It has specific functions.
However elaborate, it can only do what it's programmed
to do.

The analytical engine is why he really has his
claim to fame as the first binary computing. And the
analytical engine is simply stunning and shocking.
I'll put that up there. It's not the analytical
engine. It's the piece of the minimum analytical
engine under construction at the time of his death.

Small, experimental model. The analytical engine, in
its minimum configuration would have been 20 to 30 foot
long, 15-foot high, 8-foot in diameter. It would have
been impossible to turn by hand. He talks about the
minimum configuration would have a hundred variables.
He talks about variables. What he means is registers.
A variable is a register which can take a different
value. And the minimum configuration would be a
hundred variables. That would give you a machine the
size of a locomotive, 20 feet, 30 feet long. He talks
about machines with a thousand variables and 50 digit
registers with double precision arithmetic with a
hundred digit results.

So we can see his machines just in
conception and physical size are monumental leap, a
quantum leap, in conception, in logical conception in
relation to what the -- he was like a jack in the box.
He pops up in history, as it were, without a clue.
So the analytical engine, if I can just
stun you with the respect in which it incorporates and
embodies and almost -- I ought to be careful here I've
given his present -- it embodies almost every single
logical feature of the modern digital electronic
computer. Hah. Right.

And I challenge you to --
[ Inaudible comments from the audience. ]
I'll now list some of the features.
Separation of store and mill. The memory and the
center process is separated, physically separated --
and realize for the same reasons that the modern
computer engineers as to why this was necessary. The
capital investment in processing was too high to
distribute. They centralize and then ship the results
in and out and then ship them back. Separation of
store and mill.

Second thing is conditional branching. "If
then" statements. If a particular condition were
satisfied, it would take one other action
automatically.

It was programmable using punch cards.
There are four kinds of cards --

- number cards,

- variable
cards,

- combinatorial cards,

- and operations cards.

The
variable cards told the addresses and the store where
it must go to. The operational cards had what
instruction it could do. It had a fundamental
repertoire -- a number card was a beta card. And a
commentarial card told you how many durations to do.
So it was all programmable in this way.
Internal repertoire of instructions -- it
had automatic multiplication, automatic division,
subtraction and addition. It was user programmable.

You could screen listed instructions in any sequence
you like, you could even rate them. So it had
conditional branching integration. It had multiple
processing. So it's about multiple processes. It had
card punch output, printed output, (**) output.

These
are specific designs. This is not wishful thinking.
This is not retrospective projection from the modern
age. These are explicitly and specifically embodied in
his mechanical designs. This is not the coded
vagueness of Nostradamus. This is engineering. So
when we say he was the first pioneer of computing, this
is not a casual tribute. All these features are
specifically embodied in his machines. There's
pipelining -- and I'll explain the (**) of pipelining.

Microprogramming. You give it a single
macro instruction, say do this, and it automatically
executes the lower level instructions. These are
specific embodied instructions. So that's the
analytical engine.

I can show you some punch cards and
operational cards and variable cards. These are the
face board cards. The large ones are the operation
cards, small ones are the variable cards. You can tell
it when -- store to find the material. The cards were
based on the (**) as is well known. Which was used to
control patents of weaves, automatic control of
patented -- the patent of the textiles.

That's one of the very earliest computer
graphics. That is a portrait of Jacquard, the man
that devised and developed that thing. And that is not
an etching, it is not an engraving. It's woven in silk
using 20,000 cards in ****. And this, again, had an
interesting influence in the development of ideas.
What it did -- shaving was regarded as an
aesthetic quality which was peculiar to craft and art.

What this proved -- because you can mechanize this and
produce other copies of this -- you can show that the
industrial arts were capable of subtlety which was easy
to consider the province only of craft and art.

Now this had huge influence at the time.
It showed that such subtlety was still within the
province of mechanization at a time when mass
production was actually beginning to compete in cross
technology. And he had this hanging on his wall, and
Prince Albert saw it, and it was a very well known
celebrated piece. And precisely that because it was
mechanical and it embodied features that could easily
be regarded as -- the outside a province of a dirty old
engineering.

[Inaudible question by audience member. ]
Yes, there's one hanging in Science Museum
in the Babbage Gallery. You peer at it. I cannot
tell, even with glasses, the resolution of the weave.
It is so fine that you cannot tell -- I cannot tell
it's woven.

Okay. So that's Babbage's -- when am I
supposed to stop? 25 minutes? Fine. Okay. We'll do
more history then. Okay.
Babbage failed to build any of his engines.
He failed to build any of his engines. And the reasons
for that are still hotly debated. And his life in a
sense has become kind of a modern parable.

[Inaudible question from audience member. ]
He never completed engines. He completed
designs. He never completed any of his engines in the
metal. He built partial assemblies and experimental
pieces. And the biggest piece we saw was the
difference engine, that two-foot thing. I would say
that the fate of the rest of the parts -- he made 11 to
12,000 parts of the 25,000 needed. The rest went to
the melting pot used partly by somebody who was at
Harvard University, in fact, small assembly pieces.
But the rest went into a melting pot, and all that was
the most substantial piece he ever accomplished was
that piece I showed at the beginning, number one. It
works impeccably to this day. All the control
mechanisms are intact, and it's one of the most cogent
arguments against Babbage's detractors. They had the
****whole thing removed would work and. But there was
always this uncertainty given that he never completed
one. And that is the sort of doubt that has always
hung over Babbage's reputation.

Was he, in fact, a
dreamer? Was he an engineer of the highest caliber?
And I hope we will have some answers within the next 25
minutes.

Right. This is difference engine number 2.
That's the next thing he built. It was designed
between 1847 and 1849. That is after Babbage had
completed his major work on the analytical engine. So
he had already gone way, way beyond methods of
differences and repeated addition. He had already
managed to get machines to multiply and divide
directly, which is a strongly difficult thing to do.
And he -- during the course of the refinement of his
ideas, in the needs and demands of the analytical
engine, he realized he could build a difference engine
vastly with (inaudible).

This is like a master work.
He produced no experimental pieces for it. It was like
Mozart. He conceived of it and just produced the
design. It is also the only complete set of drawings
that was ever left, for reasons which I'll elaborate on
presently.

So that's difference engine number 2. It's
11-foot long, 7 feet high, 18 inches deep. It weighs
2.6-tons in its present form. What's missing is the
printer. What I didn't say after the business about
the tables was -- and Babbage's conception was simply
to eliminate all sources of error -- that's
calculation; transcription; typesetting, compositing;
and proofreading -- in one go through mechanization.
And the idea was that the unerring certainty of
mechanism would ensure that there were no errors in
calculation.

If you could incorporate a printer integral
with the machine, mechanically coupled to it -- that
is, to eliminate the human from the information loop
completely -- you set the initial values, you turn the
handle, what comes out is printed results. Then you
not only solve the issue of transcription, but the (**)
of typesetting. And because of the method of finite
differences, you will also solve the problem of
proofreading. With each result, depending on the
previous results, if the last result is correct, you
have a high degree of confidence that everything else
is.

So you only need to check one value.
So by using method of differences and using
automatic computation --

[Inaudible question by audience member.]
Great. Absolutely. Having one copy is
pointless because the whole point is to have a medium
of communication. The machine does not only print a
checking record in hardcopy on a print roll. What it
does is impress the results on stereotype plates of
soft metal from which printing plates could be
produced.
Now the bit that is missing over there is
the printer. Integral to the concept of this engine is
the notion of an automatic integral printer. And the
bit that's missing there, for political reasons -- we
couldn't raise the money in time for the anniversary --
is there.

And I will show you presently the first --
we're now building the printer through kind benefactual
(***). We're also building an entire replica of this
engine and printer for his house. And we have just
done the trial assembly in the last few weeks before I
came of the printer, and I will show you first images
ever of the printer -- of the trial assembly of the
printing maker. It's massive. It's more complex.
It's more interesting than the engine in many respects.
And the answer is it not only produces a hard copy but
allowed you to produce a stereotype plate which using
the conventional printing press, you could replicate
results.

Okay. I haven't quite finished saying what
this is (**) about. Okay. That's the machine. It has
8 columns of finger wheels. Numbers are represented
on -- numbers are stored and operated upon (***) figure
wheels. And I'll show you picture one presently. It's
operated by turning a handle. That operates through a
cam stack. There's your microprogram.

You turn the
handle and say calculate the next value. The cam stack
translates. That's 14 conjugate cams -- the geometric
inversion of each other -- 14 conjugate cams translates
circular motion into lifting and turning motions. They
intermate in lifting and turning signal the motions
required for the method (***) of differences allow you
to add a number from the right-hand column to the next
column, to the next column, so on.

So you're into the
initial values from a table that you calculate by hand.
And every time you turn the handle after that, you get
the next result which appears in the last column. So
the information progresses from right to left.

Now, at any given time -- so the units on
the bottom, the 30-digit numbers represented in the
column, that's a register -- the units at the bottom
tens, hundreds, so on all have top 31 digits. So the
constant difference, the last difference -- if you're
using a set of polynomials on the last one -- that
keeps its own value. It adds that number to the next
one, next column, next column, next column, so on
without a given line. Now, at any given time you've
only got two columns that are effective. If you've got
want eight columns in the machine, you've got only two
columns working.

If you're adding one to one -- the first
column to the second, second to the third. So during
the cycle, column one will add to column two. And then
column two will add to column three and so on. At any
given time, only 25 percent of the machine is working.

What do you use with pipelining? He adds
columns 1, 3, 5, and 7 to columns 2, 4, 6, 8 in the
first half cycle and columns 2, 4, 6, 8 to the odd
columns in the second half cycle. You can then extend
the machine to 14 differences and the cycle time is
independent of the number of differences. And as long
as you offset the initial values, you have an (**) of
pipelining. 1847.

[ Applause by the audience. ] I trust that
applause is for Babbage and not for me.
So we've got microprogramming, we've got
pipelining. Okay. The mechanics of it, I'll go into
presently. And I assume you're perhaps more interested
in that than in the history. But, sorry. Tough.
You're going to have to live with the history. What
else about it?

Okay. That's one of the figure wheels. It
has four **decades. The reason is he needs big wheels.
He needs big wheels because he has to have security.
They are a very secured mechanism. The whole thing is
premised on the fact this machine cannot error. Now,
Babbage -- he has three separate security mechanisms --
he challenges you. He says you can walk up to this
machine, and it will calculate correctly. It will jam,
it will break, but it will never deceive. And he's
challenging you during an operation to walk up to the
machine and try and derange those wheels.

Now that's a
rather startling thing because if you've got a wheel,
whether or not it moves depends on whether it's added
to. It can be added to in two ways. From the wheel on
the right of it on the column on the right, giving off
a number to it. Or it can receive a carry from below.
And because -- whether this wheel moves or not is data
dependent. The wheel cannot know. You cannot know in
advance whether to free it up. So what you have to do
is free it up for the window in which can either accept
the number from the right or the number from below.

You would think that during that window you could
derange it, but you can't. It is designed only to
accept information from legitimate sources. And we
didn't actually fully understand the mechanism by which
that happened. But because of the historical
integrity -- which is something I haven't spoken
about -- of this construction was such that we
replicated even things that we didn't understand. And
it was only through the course of assembling this
machine that actually we understood the monumental
subtlety of the way he had accomplished that. And I'll
show you the part that actually allows that to happen.

So the answer to the question that it (**)
unknown, why did Babbage build so big, the other
machines that are smaller that were built
subsequently -- the reason is security mechanism.
Okay. That's to give you some physical
scale. That's Rich Crick, and I'll explain about the
mega-flop presently. Well, I'll do it now. You turn
the handle. That's a construction in public view. The
public could speak to the engineers as they did it.

That's Rich Crick; that's Barry Holloway, the two
engineers who had a major role in doing it. Okay.
When you turn the handle, the machine performs in one
cycle seven 31-digit additions. Right? It performs
six calculations a minute. So one calculation takes
ten seconds. So one crick is ten -- one crick is seven
31-digit additions in a minute. And that's the -- you
need a multiplying factor to get that in the mega-flops.

Okay. What was the informational data from
which we -- which we started this to life? Babbage
left a complete set of drawings. There were twenty
drawings and four tracings. That is the one that is,
perhaps, most evocative of the shape of the machine.
It's BAB A-163.

One thing you may notice is that the handle
comes out from a vision slightly below the main shaft
of the bevel. You look at the next drawing, you can
see the handle comes out directly from the main shaft.
(**inaudible** we could afford **) When engineers
first looked at that -- people who weren't Babbage
freaks -- looked at that drawing, they didn't actually
understand how it worked. In fact, neither did we at
that stage. And they looked at all these numbers of
(**) and said it would be impossible to turn the
handle. These were people who he brought in for
advice, so he had to take the advice. None of the
Babbage zealots could possibly conceive that their hero
could have made a mistake of such fundamental -- you
know, such a fundamental mistake. So they abided by
the advice ***and we could afford introduction hearing.

It turned out the engineers were right but for totally
unforeseen circumstances. If we built the engine as
Babbage had designed, we would not have been able to
turn the handle. But nothing to do with friction.
I'll explain that presently. So the displacement of
the handle -- you can see it comes out one below -- is
to do with the form of introduction given. Now, one of
the principles of the whole issue is that any variation
in the design, any modification of the original design,
had to be reversible. Otherwise, we would invalidate
the historical -- we had to resist the charge: You
built Babbage's engine, but Babbage could not have. It
would have defeated the purpose of doing so. And as we
could say Babbage could have done this but possibly by
other means.

So the machine was built out of bronze
cast -- gunmetal, cast-iron, and steel. We did
composition analysis on 1832 metals to find the best
match. And there's only one instance we used a metal
of steel -- a spring steel of a grade that Babbage did
not have. And that doesn't affect whether or not the
machine works. It only affects how fast you can drive
it. It's an impact tooth that takes quite a hammering.

So the -- we went -- the historical integrity was
extended to the point of actual -- of any materials.
Now, the point about this drawing is that
you can see that it, in a sense, it logically
completely defines the machine. Not this particular
drawing, but a set of drawings. The shapes of the
parts are known. The intention is known, but there is
insufficient information. You can't give a drawing
like that to a workshop and expect them to make it.
There is insufficient information. There are several
categories that are missing.

Firstly, choice of materials. He doesn't
tell you what the stuff is made of. He doesn't tell
you anything about power and sync, the precision with
25 which parts are to be made. He doesn't tell you
anything about finishing or methods of manufacture.
Now, so these had to be provided by knowledge of
nonessential machine practice. Tolerancing is a
complete red herring. Tolerancing only has meaning if
there is standardization. Right?

The fundamental notion of tolerancing -- I
mean, you cannot make a nut in Manchester and a bolt in
London and expect them to fit unless there's some
method of standardization. Now, there was no
standardation in those times. Two lathes in the same
workshop would have different master screws. You
couldn't cut the same thread a nut in one and a bolt in
the other which is why he was confined to one component
manufacturer.
We used 46 separate subcontractors.

Babbage used one subcontractor, Joseph Clement. Joseph
Clement made 11,000 parts in ten years. We made 4,000
parts in six months using 46 separate specialized
subcontractors.

We unashamedly did not use
contemporary tooling. We used modern manufacturing
techniques. We used numerically controlled machines
and computer controlled machines to produce the repeat
parts. But everywhere we were absolutely scrupulous to
ensure that no part was made with more precision than
25 we know from measurements Babbage was capable of
achieving but possibly by other means. So that's our
defense.

We welded where Babbage would have forged,
and we dressed the welds to make it look like a (**).
Not to deceive but to give the visual and the
authenticity of the appearance of the machine.

We could have cast the figure wheels
instead of machining it, and we did so to get the
bright finish. We paid 25 extra pounds to do that so
that when the machine was looked at -- because 90
percent of the message of this machine when people view
it is not to do with the specifics of the
technicalities, it's actually what does a 19th Century
machine look like? What was it the Victorians never
saw?

Okay. Now, there are several interesting
things about the drawings. One is there are errors in
them, and there's a serious curatorial dilemma. If you
make a deviation from the design, then in what respect
can we claim we built Babbage's engine? If you do not
make any deviation from the design, in full knowledge,
the engine is not going to work. Why build a piece of
sculpture?

And there are various categories of error.
There are redundant assemblies. There are assemblies
which are exquisitely beautiful and perform -- do
absolutely nothing. There are (**) assemblies. These
are all to do with boundary conditions. All the errors
usually occur on the boundaries. For instance, I'll
get into that later.

I'll show you the most obvious one. There
are inconsistencies in dimensioning. There are the
same part depicted in different dimensions on two
drawings. You have to resolve that. You cannot say
we're going to make it the way Babbage intended. If
the same part is -- what do you do? You make it half
way between? You may do the same kind and try to -- I
mean, you have to resolve that.

And so one of the big
learning issues of this project was you cannot regard
these drawings as some kind of sacrosanct ideal of
perfection that -- from which any deviation would
impugn the historical integrity of the thing. You have
to -- what became very clear to us is we were resuming
a project that had been intimate a hundred and 40 years
later. This was the continuation. If Babbage had
taken these drawings of the drawing board and gone to
the workshop, he would have hit exactly what we hit.

So the issue was not what are we violating by making
any design alterations. The question is, what would
Babbage have done when he found this? And we applied
no solution that we had not found Babbage had used
elsewhere. He never uses slotted holes. He never uses
grub screws for adjustment. These are monolithic
machines. There is no possibility of debugging this
machine. You cannot isolate the drive from the
calculating section.

If you wanted movement, it makes
a fixed link -- if you wanted to another movement, you
make another link. There is absolutely no
adjustment -- splitting them up is a total nightmare.

They had never done it. They had never thought of
(**). So when the machine jammed solid, which part of
its error detection. So if it's jammed solid, you
don't know where to start. There are no test points.
You cannot isolate the drive. You go with a
screwdriver somewhere and you fiddle and you hope for
some play. If there's no play, you go further down the
machine. When you find some play, you work backwards
until there's no play and you then look. It's
absolutely hair raising.

There is no method -- they
had never built a machine of this complexity. I
absolutely believe if they had done so, they would have
used the modular construction of some kind. So we were
breaking new ground. And what became very evident is
we were actually continuing in intimate process. We
were not actually building -- we were not actually --
there was an absolute interaction between what we were
doing. This was not the distance of history working
through, as it were, Diachronical kid gloves.

Okay. Just to give you some example of one
of the issues we had to resolve. Okay. The printer
that's being built is this huge section on the right
here which is part of the control mechanism of the
machine. This is a digression. I know there isn't
time for it. I say the printer is part of the control
mechanism.
If you're turning the thing -- you set the
initial values up -- everything -- from the moment
you've turned the handle, the machine no longer in the
state you've set it up. It is now in an unknown state.

If you overrun -- the printer gets to the end of the
page -- if you overrun, you have it. You have to redo
the whole thing because the machine will then be set up
to produce the first wrong result in the beginning of
the next page. Now, you're at this end of the machine;
the printer's at that end of the machine. You cannot
counting -- you have no index card. The machine has an
index card. It knows how many calculations. But the
printer knows when it's got to the end of the page.
What it does is drop a ball into a scoop which moves,
pulls a lever as if he's a catgut which runs along
under some pulleys which goes up into a scoop cam. And
all you do is turn. And when it gets to the end of the
(**) suddenly the hand becomes free, the drive is
broken through a scoop clutch and the machine freezes
in precisely the state it's needed to change the plate
and resume for next time.

[Inaudible question from audience member. ]
Is that a reference to Microsoft again?
Okay. Just to give you some idea of some
of the informational issues we had to resolve. You can
see that the pitch, that's a separation of those
columns is all the same (microphone off speaker,
inaudible) second and the third. Excuse me. The
separation between the second and third column is
different. Is that significant?

We're building
Babbage's engines, are we going to build with that
space there? We think, well, hang on a minute there's
no coupling. Is there some special significance to the
first two columns? Well, there isn't if we understand
that these are just differences. They replicate the
mechanism. Well, we think, okay. If you see a planned
view of this thing -- if you look down from the top
would this resolve the issue? And, indeed, you look at
the planned view -- why is there no planned view?
There. There's the planned view.

You can see how monstrous the printer is.
It weighs another three tons, estimated, which brings
it up to the five. If you look at that, you can see
that there is a discontinuity in precisely the same
place. That's looking at the engine from the top.
We're looking between column 2 and column 3. And you
can see there's a discontinuity there. There's a
little (**) there.

Well, we puzzled long and hard. We didn't
want to violate it unnecessarily. But equally, we
didn't want to build something we didn't understand.
We puzzled over this and the conclusion we came to is
that the draftsman had started on the left on, say,
Monday, and he'd worked all the way and he started on
the right on Thursday and he got to the middle and
said, the hell with this, I'm not doing this over. And
he got the pitch wrong. And there was no more
significance than layout area than a drafting error.
There's no other conceivable explanation for this.

But those were angles. We took this very
seriously. Was there some deep significance to the
separation? Okay. That's one of the more obvious
ones, but more there are vastly more subtle ones of the
kinds of --

Okay. That's the cam stack when you check
the wheel. That is another drawing that indicates the
kind of absence of information. There is no -- it
describes the drawing, you can logically understand it.
But there is no information of choice of materials,
method of manufacture, finish and tolerancing.
Tolerancing is the red herring as I mentioned.

Okay. Now one of the security mechanisms I
should mention -- because it has sort of another
analogy to electronic computing -- is the way the
machines lock. I don't even see there's a wedge.
There's a wedge which drives it. Actually, there's a
better drawing of that so I can expand it in the next
one, I believe. Yes. That is the guts of the engine.
That is what's clever about it. Now, the calculators
up to that time had six to eight digits in them. Okay.

The problem is carriage of tens. How do you do that?
That's the actual guts of the machine, and why it's so
elegant, why you could extend registers to 30, 50, and
a hundred digits is because it solved the principle of
successive carry. All the calculators up to that day
had six, eight digits, maybe up to twelve. And the
reason for that is -- the worst case is if you have a
row of nines and you add a one, you have to propagate
the carry, ripple through domino carry it's called.

Now, if you were running with dials, and you've got
99999 and you turn the last one, you have to actually
drive those wheels from the force derived from the
last turn. They didn't have the materials. They
couldn't do it. There was no success for progression
way to.
What he did was, he separated the addition
cycle from the carry cycle by using memory. He used
latches. I mean, he talks about one-unit memories.

And he did this entirely mechanically. Now what's
clever about this machine is once you separate addition
from carriage, you've actually solved the problem of
force. But you've distributed in time bites. You
don't apply all the force in one go at one point.
You're distributing time and that's -- the most
visually dramatic and attractive feature of this engine
as you will see on the video is the this progression,
this dancing D. N. A. of this rippling helices that you
will see.

Now, this is the mechanism. That's the --
you can see that's the planned view of the helix, that
little fairground thing with the **loggans on the end.
And one of the security mechanisms is -- that's a
figure wheel. The way you lock it is you have a wedge.
It's like a sword blade which runs up the column and
jams itself between the figure wheels, and it locks
them. That's the wedge here, plan of the wedge. You
can see the wedge. The wedge would drive it. So the
wheel is only freed within the window in which it can
receive information from a long side of below, and it
comes and it's free to move. It's locked in other
respects during the window which it's able to move.
And that thing drives its way.

And the reason the
machine couldn't be turned is because the pressure
angle of a cam that drives that thing -- because it
comes in and goes out very quickly -- so that's the
steepness of the side. But the thing to follow it was
too steep, and you actually couldn't drive the handle
past this thing. And I'll show you a picture of that.

The point about this is that one of the security
mechanisms is this lock. Now if the machine -- if a
wheel deranges very slightly and the wedge can still go
in, you've got a pulse shaper. It restores the slight
derangement. If it goes up to two and a quarter
degrees out, it's going to come in onto a cog, and it
will jam. And that says this wheel is in indeterminate
state. It's no longer a digital machine, it's an
indeterminate state. And that is how the controller --
we saw the half moons with the roller that sandwiched
on the first difference engine. The weights through
the wedges and controls. And that slapping sound
you'll hear is actually the locks coming in and out.

The reason for that drawing is to show you the
difference between the Babbage specification of that
part -- which is that part up there, which is a carry
lever -- and the amount of information you need to
specify a modern piece pod. That's the most complex
piece. There are 210 of those, left and right handed.
And that's the amount of information you need to
specify to the modern machine tool shop. You can see
the sparseness -- the richness of Babbage's drawing
metals -- the sparseness of manufacturing information.

Now we had to produce these takings to drawings and
produce piece pod drawings for all 4,000 parts of this
thing. And that took another 50 drawings to do, and
every one had to be specified. That's -- again, that's
a modern drawing. That's the part up there on top
right. And that's the technical of the 50 drawings
that were made. That's 50 just for the calculating and
another 50 drawings for the printer.

Okay. That's the same -- that's the plan.
That's the -- okay. There is a major error. There is
a major, major error in the design. It is not a
logical error, although we didn't know that at the
time. I'll go back to this mechanism.
That is the guts of the engine. This
figure wheel column adds to that figure which is an
intermediate sector wheel so you don't get a
nondestructive transfer. To have a wheel and you
rotate it to zero, it will transfer its number to the
next wheel but you've lost the numbers so you have to
restore it. But the intermediate wheel it stores the
number, uncouples from the other one, and then restores
it. And you'll see that cycle on the --

There's a fundamental error. We don't have
a pointer. You can see that curved nook over there on
the wheel just up there. That nook is what is nudged
when a wheel goes above ten. This is a successful
carry mechanism. So when a wheel goes above ten, a
nook knocks that curved nook and it latches through an
indent. I'll show you a computer animation of it
presently. The point about it is that that mechanism
can only work if the wheel turns, for you,
anticlockwise.

The staggering thing in the designs is
that the wheels go the wrong way. The mechanism won't
work. It is absolutely fundamental. This created a
terrible crisis. But the issue is was he using some
(**) form of arithmetic that we didn't understand? Was
this a method of preventing industrial espionage? Was
the error deliberate? And we wracked our brains about
what the solution was.

There are three solutions. You
can lengthen the cycle.
[Interruption by moderator re time.]
Let's snap along. What was I talking
about? Wheels going the wrong direction.
Okay. There are several ways you can do
this. You can make the wheels go the other way by
changing the control mechanism. You can insert an
intermediate wheel and reverse the direction. Or you
can mirror image each alternative access. You can see
the thing is biased to the right. Each alternative
access you can bias to the left. The implication of
biasing it is -- mirror imaging it is -- it introduces
a 2 and a quarter degree shift. And the reason for
that is peculiar, one is something Babbage never
foresaw. If you join the center line of that thing to
that thing, you'll find that the center line does not
go through the middle of the tooth. It goes to the
right of the tooth. So if you mirror image it, you get
a tooth where there should be a gap. The result of
that is you have to turn the thing 2 and a quarter
degrees and the problem is how do you know the damn
thing would work?

And so that was the -- the problem
was a major design. It's not a logical error; it's a
layout error. Second thing is what is the solution?
The solution is mirror imaging. So we actually had to
redesign the whole thing and take account of the 2 and
a quarter shift all the way through.

[Question by audience member: Do you have a
3-D model? ]
I'll show you. We built a trial piece to
verify the fundamental mechanism. Sorry, it's a back
to front slide. It adds a two-digit number and takes
account of carry. Now, it's not automatic. You
manipulate the rods and levers from the top to actually
execute -- the cycle has 11 separate stages in it. And
this is what we built which is the first -- it's
actually the engine that we built to verify this new
configuration.

We learned something very fundamental
about the psychology. Okay. We were also trying to
get funds that I haven't spoken anything about the
politics and what we're going to do. I mean, this is a
bunch of lunatics in a back room trying to do this
stuff. And the question is how do you attract
attention? And we discovered something fundamental
about the psychology of what we were doing. We found
that if you want to convince somebody that something is
made accurately and precisely, you make it shiny. And
that's a legacy of instrument making. Where precise
things get polished.

Now, we got practically no attention for
this project. We put in for the trustees, and they
were sort of dutifully respectful of us. So we
polished the top plate. We got on television. They
ran credits passed it, they put on the (**). Trustees
wanted to give us money. So -- okay.
There the beautiful -- the beautiful --

okay. This is the helical mechanism that I showed you,
(inaudible). It's an object of beautiful elegance in
this machine. That's the helical mechanism which does
successive carry. The (**) is very interesting so I'm
going to tell you about it. What happens is, the thing
in its addition cycle adds all in one go. All the 31
wheels are meshed to 31 (**) and the addition is done
all at once. If a wheel in any decade exceeds ten, it
latches -- the thing using an indent. What happens is
that each of the positions need to be pulled --
right? -- in succession. And how it pulls it is,
tipping the thing that -- as the thing -- as the wheel
turns, it knocks the latch. The latch has a lever.
The lever puts it in a particular position. What
happens with this thing, as it rotates, it pulls each
position in turn. It is placed in the fixed angular
position, and pulls each lever. The way it pulls it is
it sweeps the position. If the lever is set, that's
(**), it's intersects and the locaters of the two
intersections nudge it and it goes into the next wheel
up. If it's not set, it misses it completely. So
there's a conditional pulling which does successive
carry. It's a ripple through carry so bottom carry can
progress all the way up, and it can handle secondary
carries, carries that are (**) carries because it
rotates twice.

So that's how the carry mechanism works.
Now, the force on that thing at any given time is never
more than it takes to move one wheel. That's how you
can extend these things. Okay. I think what we should
do -- let me just check to see what's there, and I
think we should run the video. That's another piece of
(inaudible) -- okay. Just -- back of the -- that's the
carry mechanism assemble, the back of the machine. And
if you think that's impressive, have a look at that.
And if you think that's impressive, have a look at
that. And if you think that's impressive -- that's the
(**) version. That's the back of the machine with the
double helices which you'll see. Okay. I'll -- I
suggest what we should do now is probably run the
video, and you'll see the machine running.

Sorry. There was a question which I didn't
finish answering.
[Question from audience member: How often
did you run it? ]
We ran it twice a day as a matter of
routine during the anniversary year of the exhibition,
and now we run it to anyone who expresses interest.
[Brief inaudible conversation with audience
member. ]
Sunday is difficult because we have
explainers who do this on weekends. Any weekday,
either myself or my assistant will demonstrate the
machine to you, even if you're an individual. You
don't need to be a group or by arrangement. If we're
there, we'll do it. We're going to change that. Now
that we're building the printer, we're going to
actually -- I'll show you the slides of the printer --
we were planning on having the printer run and
printouts using conventional 1838 printing press and
get results out. And we tend to do that as fixed
demonstrations. There well be fixed demonstration
times.

So I think that's the end of the -- is that
the end of the televised proceedings? Seems so. Do we
need a decision about whether you want any more? Do
you want to hear about the printer or not?

[ The audience: Yeah. ]
Okay. Right. We can relax now.

We can talk dirty. Okay.
This is to give you some idea of some of
the information density. The photographs -- the images
I've shown you before are some of the best ones.
They're the ones that are most evocative in shape and
ones that are most meaningful in terms of internal
mechanism. But not all of them are so immaculate.

That's an example where they didn't have automatic ways
of producing tracings. So what they do is draw one
view over another view and over another view and rely
on dotted lines to present hidden edges. And that's if
you like -- the point is, the thing becomes
impenetrably dense. And there were some issues which
we actually could not resolve.

The question from that
drawing is whether the framework is one piece, is one
cast bed, or that it's made up of multiple things.
And, actually, we did not -- we were not able to
resolve that. So we had to make decisions based on
knowledge of 19th century machine (**). We were
fortune in having (**) with Michael Right, who steps
right out the 19th century. Instead of phoning
Babbage, we would just go talk with this guy, and he knows
everything there is to know about 19th century
machines.

When we walk into his basement, it's like I
can see Clement. So we relied on him very heavily on
what parts, what materials Babbage would have used,
what's the composition of gunmetal and all that stuff.
And, you know, what size castings would they be capable
of making. You see, they didn't have planing machines.
They didn't have long bit planing machines. Now you
just make something very rough and plane it and get the
precision that way. But the casting techniques were
vastly more evolved than ours. Because they didn't
have planing techniques, their casting was vastly
better. So the question is, we may not be able to cast
beds that precisely. But what we do is plane them. So
what we do is we make them out of separate sections.
Off the air.